Caring enough to listen, then communicating that you actually did listen by repeating some of the words they said back to them. How is that manipulation?
In this context, wouldn't manipulation be where you don't listen then say some words which try to (falsely) communicate that you did listen?
(Contrast: not listening, and showing that with "I ain't reading all that. I'm happy for u tho. Or sorry that happened". Contrast: actually did listen but they think you didn't, leading to "I'm so angry about X!" / "How come X is bothering you?" / "I am not bothered by it, I am angry about it!, weren't you listening?!" poor communication. Where "what about X is making you angry?" instead reflects the feelings they said, showing you heard what they said, but does not seem manipulative).
There is a nuanced, but important point to make here regarding responsibility.
One of resources I watched (a therapist) described therapy as 90% active listening. It's important to be aware of that proportion and the tendency of people to really open up when someone is truly listening.
For example, I was at a bar talking to a stranger when they had to take a break. They were on the brink of tears because they were talking about something that was so deeply meaningful to them[1]. I missed the flag and will always think back to my responsibility - just to pick up on those signs and ask the person if they're doing ok. There's a vulnerability index which I like to reference that conceptualizes some of this.
The difference between open inquiry and probing/drilling is an important distinction to keep in mind when listening too. Laying some of these skills on too thickly can come across as more of an interview than a conversation.